Piezoelectricity is the ability of certain crystalline materials to develop an electrical charge proportional to an applied mechanical stress. The converse effect can also be seen in these materials where strain is developed proportional to an applied electrical field. It was originally discovered by the Curie's in the 1880's. Today, piezoelectric materials for industrial applications are lead based ceramics available in a wide range of properties. Piezoelectric materials are the most well known active material typically used for transducers as well as in adaptive structures.
Virgin ceramic materials must be first poled to utilize their complete piezoelectric effect. Poling consists of applying a high electrical field to the material. During the poling process the crystal dipoles in the material are aligned with the applied electrical field and the material expands in the direction of the electrical field. By applying a field in the opposite direction, strain of opposite sign is observed. If the magnitude of this opposite field is increased, the material first depoles and finally repoles.
Poled piezoelectric material is considered transversely isotropic, i.e.: one plane is isotropic while the out-of-plane direction has different properties. The standard coordinate convention adopted by the IEEE [IEEE Standard on Piezoelectricity, 176-1978] assigns the 1-2 plane as the plane of symmetry and the 3-direction as the-out of-plane poling direction. For a small applied electrical field, the response of the piezoelectric ceramic can be modeled by the following linear piezoelectric constitutive [Jaffe, B., Cook Jr., W. R., and H. Jaffe, 1971, “Piezoelectric Ceramics”, Academic Press] expressed in engineering matrix notation as:
                              {                                                    S                                                                    D                                              }                =                              [                                                                                s                    E                                                                                                              (                      d                      )                                        T                                                                                                d                                                                      ɛ                    T                                                                        ]                    ⁢                      {                                                            T                                                                              E                                                      }                                              (        1        )            
where D—electrical displacement, S—strain, E—electric field, T—stress, ∈T—constant stress (unclamped) dielectric, d—induced strain constant, sE—constant field compliance.
Mechanical compression or tension on a poled piezoelectric ceramic element changes the dipole moment, creating a voltage. Compression along the direction of polarization, or tension perpendicular to the direction of polarization, generates voltage of the same polarity as the poling voltage. Tension along the direction of polarization, or compression perpendicular to the direction of polarization, generates a voltage with polarity opposite that of the poling voltage. These actions are generator actions—the ceramic element converts the mechanical energy of compression or tension into electrical energy. This behavior is used in fuel-igniting devices, solid state batteries, force-sensing devices, and other products. Values for compressive stress and the voltage (or field strength) generated by applying stress to a piezoelectric ceramic element are linearly proportional up to a material-specific stress. The same is true for applied voltage and generated strain.
If a voltage of the same polarity as the poling voltage is applied to a ceramic element, in the direction of the poling voltage, the element will lengthen and its diameter will become smaller. If a voltage of polarity opposite that of the poling voltage is applied, the element will become shorter and broader. If an alternating voltage is applied, the element will lengthen and shorten cyclically, at the frequency of the applied voltage. This is motor action—electrical energy is converted into mechanical energy. The principle is adapted to piezoelectric motors, sound or ultrasound generating devices, and many other products.
FIG. 1a. Schematically depicts the generator action of a piezoelectric element as known in the art.
The piezoelectric material has a considerable impact on the achievable performance of the transducer. Commonly used piezoelectric materials are based on lead zirconate titanate (PZT) ceramics.
Assuming that a PZT element is directly used as a transducer, the significant material parameters can be outlined to provide the material figure of merit. There are many factors that influence the selection of the PZT composition. The constitutive equations for a linear piezoelectric material under low stress (T) levels can be written asx=sDT+gD  (2)AndE=−gT+βXD  (3)
where x is the strain, D is the electric displacement, E is the electric field, s is the elastic compliance, and g is the piezoelectric voltage coefficient given as
                    g        =                  d                                    ɛ              0                        ⁢                          ɛ              X                                                          (        4        )            
Here, d is the piezoelectric constant and ∈ is the dielectric constant. The constant β in eq. (3) is the dielectric susceptibility, and is equal to the inverse dielectric permittivity tensor component. Under an applied force F=T·A, (where A is the area), the open circuit output voltage (U) of the ceramic can be computed from eq. (3), and is given as
                    U        =                  Et          =                                    -              gTt                        =                          -                              gFt                A                                                                        (        5        )            
where t is the thickness of the ceramic. The charge (Q) generated on the piezoelectric ceramic can be determined from eq. (2) and is given as
                              D          =                                    Q              A                        =                                          E                                  β                  X                                            =                                                U                  ⁢                                                                          ⁢                                      ɛ                    0                                    ⁢                                      ɛ                    X                                                  t                                                    ⁢                                  ⁢        or                            (        6        )                                          Q          /          U                =                                                            ɛ                X                            ⁢                              ɛ                0                            ⁢              A                        t                    =          C                                    (        7        )            
where C is the capacitance of the material. The above relationship shows that at low frequencies a piezoelectric plate can be assumed to behave like a parallel plate capacitor. Hence, the electric power available under the cyclic excitation is given by eq. (8) as follows.
                    P        =                                            1              2                        ⁢                                          d                2                                                              ɛ                  0                                ⁢                                  ɛ                  X                                                      ⁢                          F              2                        ⁢                          1              A                        ⁢            fP                    =                                                    1                2                            ⁢                              CV                2                            ⁢              f                        =                                          1                2                            ⁢                              (                                  d                  ⁢                                                                          ⁢                  g                                )                            ⁢                              T                2                            ⁢              Vf                                                          (        8        )            
where V=A×t is volume of the piezoelectric generator
Under certain experimental conditions, for a given material of fixed area and thickness, the electrical power is dependent on the d2/∈X ratio of the material.
A material with a high d2/∈X ratio will generate high power when the piezoelectric ceramic is directly employed for harvesting energy.
FIG. 1b(i) depicts the construction of a single element transducer and FIG. 1b(ii) depicts a multi-layered transducer.
In a multilayered construction of FIG. 1b(ii), the same force F is applied to all the layers. However, due to the smaller thickness of each layer, the voltage developed in each of the layer, (which is the voltage developed on the entire structure, as the layers are electrically connected in parallel) is lower. Electrically connecting all the layer in parallel increases the capacitance of the structure.
FIG. 1b(iii) depicts a preferred embodiment of a multilayer PZT generator wherein the polling directions of consecutive layers are reversed. In this embodiment, a common electrode is used between two, oppositely oriented layers.
The review article “Advances In Energy Harvesting Using Low Profile Piezoelectric Transducers”; by Shashank Priya; published in J Electroceram (2007) 19:165-182; provides a comprehensive coverage of the recent developments in the area of piezoelectric energy harvesting using low profile transducers and provides the results for various energy harvesting prototype devices. A brief discussion is also presented on the selection of the piezoelectric materials for on and off resonance applications.
The paper “On Low-Frequency Electric Power Generation With PZT Ceramics”; by Stephen R. Platt, Shane Farritor, and Hani Haider; published in IEEE/ASME Transactions On Mechatronics, VOL. 10, NO. 2, April 2005; discusses the potential application of PZT based generators for some remote applications such as in vivo sensors, embedded MEMS devices, and distributed networking. The paper points out that developing piezoelectric generators is challenging because of their poor source characteristics (high voltage, low current, high impedance) and relatively low power output.
The article “Energy Scavenging for Mobile and Wireless Electronics”; by Joseph A. Paradiso and Thad Starner; Published by the IEEE CS and IEEE ComSoc, 1536-1268/05/; reviews the field of energy harvesting for powering ubiquitously deployed sensor networks and mobile electronics and describers systems that can scavenge power from human activity or derive limited energy from ambient heat, light, radio, or vibrations.
In the review paper “A Review of Power Harvesting from Vibration using Piezoelectric Materials”; by Henry A. Sodano, Daniel J. Inman and Gyuhae Park; published in The Shock and Vibration Digest, Vol. 36, No. 3, May 2004 197-205, Sage Publications; discuses the process of acquiring the energy surrounding a system and converting it into usable electrical energy—termed power harvesting. The paper discuss the research that has been performed in the area of power harvesting and the future goals that must be achieved for power harvesting systems to find their way into everyday use.
Patent application WO07038157A2; titled “Energy Harvesting Using Frequency Rectification”; to Carman Gregory P. and Lee Dong G.; filed: Sep. 21, 2006 discloses an energy harvesting apparatus for use in electrical system, having inverse frequency rectifier structured to receive mechanical energy at frequency, where force causes transducer to be subjected to another frequency.